Chapter 2: Q16. (page 110)

Write an equation and solve each problem. (Lesson2.3)
Find four consecutive integers with a sum of 106.

Short Answer

Expert verified

Four consecutive numbers are 25, 26, 27, and 28.

Step by step solution

Step 1. Given Statement.

To find four consecutive integers with a sum of 106.

Step 2. Consecutive integers.

Consecutive integers can be written in the form as: $x, x + 1, x + 2, x + 3, x + 4$ , and so on where x is any integer.

Step 3. Description of step.

In order to solve the problem, i.e. to find the four consecutive integers with sum of 106, take one number as x, then other three must be $x + 1, x + 2, x + 3$ .

Now, as given sum of these four consecutive integers is 106

Thus,

$\begin{matrix} (x) + (x + 1) + (x + 2) + (x + 3) = 106 \\ x + x + 1 + x + 2 + x + 3 = 106 \\ 4 x + 6 = 106 \\ 4 x = 106 - 6 \\ \Rightarrow 4 x = 100 \\ \Rightarrow x = \frac{100}{4} \\ \Rightarrow x = 25 \end{matrix}$

Thus, value of x is 25 and other numbers are

$\begin{array}{l} x + 1 = 25 + 1 = 26 \\ x + 2 = 25 + 2 = 27 \\ x + 3 = 25 + 3 = 28 \end{array}$

Therefore, required four consecutive numbers are 25, 26, 27, and 28.

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Write an equation and solve each problem. (Lesson2.3)
Find four consecutive integers with a sum of 106.

Short Answer

Step by step solution

Step 1. Given Statement.

Step 2. Consecutive integers.

Step 3. Description of step.

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Write an equation and solve each problem. (Lesson2.3)Find four consecutive integers with a sum of 106.

Short Answer

Step by step solution

Step 1. Given Statement.

Step 2. Consecutive integers.

Step 3. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

Write an equation and solve each problem. (Lesson2.3)
Find four consecutive integers with a sum of 106.